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cahlen/cfd-chaotic-advection

Chirikov Standard Map Lyapunov Spectrum Maximal Lyapunov exponent Λ(K) for the Chirikov standard map on T², computed with a custom CUDA Benettin kernel on NVIDIA RTX 5090 (sm_120). Part of the bigcompute.science CFD conjecture program — GPU-accelerated exploration of open questions in fluid mixing and dynamical systems. Quick Start from datasets import load_dataset ds = load_dataset("cahlen/cfd-chaotic-advection", "deep_sweep", split="train") row = ds[1200]… See the full description on the dataset page: https://huggingface.co/datasets/cahlen/cfd-chaotic-advection.

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Chirikov Standard Map Lyapunov Spectrum

Maximal Lyapunov exponent Λ(K) for the Chirikov standard map on T², computed with a custom CUDA Benettin kernel on NVIDIA RTX 5090 (sm_120).

Part of the bigcompute.science CFD conjecture program — GPU-accelerated exploration of open questions in fluid mixing and dynamical systems.

Quick Start

python

from datasets import load_dataset

ds = load_dataset("cahlen/cfd-chaotic-advection", "deep_sweep", split="train")
row = ds[1200]
print(f"K={row['K']:.4f}, mean Λ={row['mean_lyapunov']:.6f}")

What's In This Dataset

Each row is one coupling parameter K on a uniform grid in [0, K_max]:

Column	Type	Description
`k_index`	int	Grid index
`K`	float	Standard map coupling parameter
`mean_lyapunov`	float	Mean maximal Lyapunov exponent over ICs
`std_lyapunov`	float	Standard deviation across ICs
`min_lyapunov`	float	Minimum over ICs
`max_lyapunov`	float	Maximum over ICs
`fraction_positive`	float	Fraction of ICs with Λ > 0

Configurations

Config	n_k	n_ic	n_iters	K_max	Trajectories	Wall time
`deep_sweep`	2048	8192	50000	5.0	16,777,216	116.6 s
`standard_sweep`	512	4096	20000	5.0	2,097,152	5.9 s
`smoke_test`	64	512	5000	2.0	32,768	~1 s

Certifying logs are in logs/. Claim-validation artifacts in validation/ (convergence at $K=5$, convergence_k5_gpu.json). Metadata in metadata.json.

Validation artifacts

File	Description
`validation/convergence_k5_gpu.json`	GPU mean Λ at $K=5$ for 5k–100k iterations (65,536 ICs)
`validation/lyapunov_k2_ic65536_iter*.csv`	Per-iteration-count sweeps at $K=0$ and $K=5$ only

Generated by validate_claims.py — see finding claim-validation table.

Key Results (deep_sweep)

—Λ(0) = 0 (integrable limit validated)
—At literature K_crit ≈ 0.971635406: mean Λ ≈ 0.0446, >99.9% ICs positive
—At K = 5: mean Λ ≈ 0.956
—Zero NaN/Inf across all trajectories

Reproduction

bash

git clone https://github.com/cahlen/idontknow.git
cd idontknow
./scripts/experiments/cfd-chaotic-advection/run.sh 2048 8192 50000 5.0

CUDA kernel: cahlen/bigcompute-cuda-kernels (cfd-chaotic-advection/standard_map_lyapunov.cu)

—Experiment: bigcompute.science/experiments/cfd-chaotic-advection
—Finding: Standard Map Chaos Onset

Citation

bibtex

@misc{humphreys2026cfdchaoticadvection,
  author = {Humphreys, Cahlen},
  title = {Chirikov Standard Map Lyapunov Spectrum (GPU-Computed)},
  year = {2026},
  publisher = {Hugging Face},
  howpublished = {\\url{https://huggingface.co/datasets/cahlen/cfd-chaotic-advection}}
}

Human–AI collaborative research. Not peer-reviewed. All code and data open for verification.